PCA is a dimensionality-reduction technique that is helpful whenever we are dealing with high-dimensional data. In a sense, you can think of an image as a point in a high-dimensional space. If we flatten a 2D image of height m and width n (by concatenating either all rows or all columns), we get a (feature) vector of length m x n. The value of the ith element in this vector is the grayscale value of the ith pixel in the image.
To describe every possible 2D grayscale image with these exact dimensions, we will need an m x n-dimensional vector space that contains 256m x n vectors. Wow!
An interesting question that comes to mind when considering these numbers is—Could there be a smaller, more compact vector space (using less-than ...
